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Unformatted text preview: t A).
Proof.
E is obtained from In by interchanging two rows: Then
det E = −1 and so det(EA) = − det A = (det E )(det A).
E is obtained from In by multiplying a row by λ = 0: Then
det E = λ and therefore det(EA) = λ det A = (det E )(det A).
E is obtained from In by adding λ times one row to another
row: Then det E = 1 and so
det(EA) = det A = (det E )(det A). Outline Linearity of the Determinant Determinants and Invertibility Determinants and Products The Determinant of a Product of Matrices Theorem
If A and B are n × n matrices, then
det(AB ) = (det A)(det B ). Determinants and Inverses Outline Linearity of the Determinant Determinants and Invertibility Determinants and Products Determinants and Inverses Proo...
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